Amit Singer, “Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning”

/ August 19, 2022/

November 29, 2022 @ 12:00 pm – 1:15 pm

“Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning”

Amit Singer, PhD

Professor of Mathematics

Princeton University

Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules that are rapidly frozen in a thin layer of vitreous ice. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. Furthermore, the method is automatically regularized and requires minimal user interaction. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.


Biography: Amit Singer is a Professor of Mathematics and member of the Executive Committee of the Program in Applied and Computational Mathematics (PACM) and of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an Assistant Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the BSc degree in Physics and Mathematics and the PhD degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. He served in the Israeli Defense Forces during 1997-2003. His list of awards includes SIAM Fellow (2022), the Simons Math+X Investigator Award (2017), a National Finalist for Blavatnik Awards for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), Simons Investigator Award (2012), Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize for Best PhD in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.

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Tuesdays, 12pm-1:15pm

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